Binary 110111010101 to decimal – UGC NET Question

To convert 110111010101 to decimal, we expand it using powers of two. The bit pattern corresponds to 2^11 + 2^10 + 2^8 + 2^7 + 2^6 + 2^4 + 2^2 + 2^0. This sum is 2048 + 1024 + 256 + 128 + 64 + 16 + 4 + 1 = 3541. Therefore, the decimal equivalent of 110111010101₂ is 3541.

Option A:
Option A, 3521, is smaller than the correct sum. If we re-evaluate the place values, the powers of two do not add up to 3521. This number reflects a slightly different pattern of bits than the one given, so it cannot be correct.

Option B:
Option B, 3540, is just one less than the actual decimal value. A correct conversion must match the exact weighted sum of all set bits. Since the correct expansion yields 3541, this near value is not acceptable.

Option C:
Option C, 3451, changes the hundreds digit significantly. This would require a very different combination of powers of two. Because the given bit pattern clearly sums to 3541, 3451 is inconsistent with the binary representation.

Option D:
Option D, 3541, exactly matches the value obtained from summing the weights of all ones. Both manual calculation and calculator verification confirm this result. Hence, this option correctly represents the decimal value of the given binary number.